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Alex Holcombe
Polly Barr
• Charlie Ludowici
• Kim Ransley
• Ingrid Van Tongeren
William Ngiam
Fahed Jbarah
• Patrick Goodbourn


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crowding or constant time or what?

  • apparent motion, two-frame, optimal displacement is 1/4 of spatial frequency[1][2]
  • apparent motion, repetitive, optimal displacement depends on sampling rate but is constant phase? No, because[1]
  • Stereopsis: constant spatial offset until reach temporal frequency limit [3]
  • Vernier: below about 10 Hz, fairly constant spatial shif (dependent on contrast). Then, kinda temporal offset of <1 ms (saturates quickly with contrast)

What equation should we use to fit the graphs of speed vs. std dev?

In particular, what should we use to account for the curve at low speeds? Simple combo of spatial, temporal uncertainty = sqrt(sqr(spatial) + sqr(temporal*speed))

This paper (Ramamurthy, M., Bedell, H. E., & Patel, S. S. (2005). Stereothresholds for moving line stimuli for a range of velocities. Vision Res, 45(6), 789-799) has some interesting modeling and refs to earlier modeling that should be helpful.

Most of the moving Vernier papers (including all the SC Chung and Bedell papers I think) don't temporally ramp their stimulus! Only exception I know is Mechler & Victor who ramped just over 20 ms Mechler, F. & Victor, J. D. (2000). Comparison of thresholds for high-speed drifting vernier and a matched temporal phase-discrimination task. Vision Res, 40(14), 1839-1855. Absence of ramp could easily reduce the degradation caused by motion and invalidate the model's predictions for uncertainty based on velocity. None of the papers seem to address this point.


  1. Watson AB. Optimal displacement in apparent motion and quadrature models of motion sensing. Vision Res. 1990;30(9):1389-93. PubMed ID:2219754 | HubMed [Watson90]
  2. Morgan MJ and Castet E. Stereoscopic depth perception at high velocities. Nature. 1995 Nov 23;378(6555):380-3. DOI:10.1038/378380a0 | PubMed ID:7477373 | HubMed [MorganCastet]
All Medline abstracts: PubMed | HubMed